FIKUSZ

Mihály Weiner

(Rényi Inst)

Quasi-orthogonal decomposition of matrix algebras

Motivated by Quantum Information Theory, I investigate possible
quasi-orthogonal decompositions of matrix algebras. Decomposing our
matrix algebra, in particular, into maximal abelian subalgebras, is
equivalent to finding a complete system of "mutually unbiased bases"
(MUB) which is a famous open problem. However, the general case is
little studied.

In my talk I will explain the origin of the problem, its
surprising relation to such other problems as that of the existence of a
complete set of orthogonal Latin squares, some known facts as well as
some new results.